Apparatus for describing and tracing curves



Dec. 31, 1935. E. AFRICANO 2,025,842

APPARATUS FOR DESCRIBING AND TRACING CURVES Filed Aug. 4, 1934 2 Sheets-Sheet ,1

rlcana pvVeMTaR fl/ awcw/ $3 0654 Dec. 31, 1935.

E. AFRICANO APPARATUS FOR DESCRIBING AND TRACING CURVES Filed Aug. 4 1934 2 Sheets-Sheet 2 Patented Dec. 31, 1935 UNITED STATES APPARATUS FOR DESCRIBING AND TRACING CURVES Elia Africano, Turin, Italy Application August 4, 1934, Serial No. 738,547

In Italy August 11, 1933 7 Claims.

The present invention relates to an apparatus for describing and tracing curves such as an ellipse, a sine curve, cycloids, an Archimedean spiral, etc., characterized by two pairs of cranks,

the parallel axes of rotation of which are arranged in pairs in two planes perpendicular to each other and are connected to a supporting frame while means are provided for maintaining the cranks parallel during their rotation and it is further characterized by two rods each pivoted to the cranks of a pair, at points situated at a predetermined distance from the axis of rotation of these same cranks. The point of intersection of the said rods being materialized by an intersection member sliding upon the two rods, each point on the said intersection member describing curves identical to those described by the point of intersection of the two rods so that a tracing point or an operative tool secured to the said intersection member will serve for tracing or materializing these same curves on a piece of work.

One embodiment of the subject of the invention is illustrated simply by way of example and diagrammatically in the accompanying drawings in which:-

Figure 1 illustrates the method for the geometrical construction of an ellipse followed by the apparatus according to the present invention.

Figure 2 shows diagrammatically in plan view the apparatus employed as an ellipsograph.

Figure 3 shows in detail the member applied to correspond with the point of intersection of the two rods.

Figure 4 shows one of the cranks in detail in plan view and in vertical longitudinal section.

Figure 5 shows diagrammatically in plan view the apparatus employed for tracing sine curves.

Figure 6 shows in detail in plan view and in vertical longitudinal section a modification of the crank made in order to adapt the apparatus for describing an Archimedean spiral.

Figure 7 is a plan view showing the apparatus fitted with a dividing device.

The apparatus will first be described in its application to an ellipsograph.

It is known that an ellipsograph can be constructed geometrically (see Figure 1) by tracing, 50 with a common centre 0, two circles of radius a and b equal to the two half axes of the ellipse to be constructed, by then tracing any radius p which intersects circles a and b at M and N respectively and by finally tracing the intersection 55 P01 the straight lines A, A, and B, B, which project the points M and N respectively upon the two perpendicular axes a: and y passing through 0.

This point P is a point on the desired ellipse. In fact if is the angle formed by the radius 41 with the axis :1: we have: x=a cos and 11:12 6 sin which is in fact the parametric equation of the ellipse having half axes a and b.

Now the apparatus according to the present invention reproduces mechanically precisely the geometric construction of the ellipse described 10 above.

This apparatus comprises (see Figure 2) two pairs of cranks I, l, and 2, 2, the axes of rotation I, 2', of which are parallel and are arranged in pairs in two planes at right angles to each other 16 and which when projected in plan give the perpendicular axes a: and y intersecting at o.

The axes of rotation of the cranks are supported in a fixed position by a frame formed for example by a supporting plate 3. With the object of 20 preserving the parallel relation between the various cranks during their rotation, each axis of rotation of these cranks is provided with a toothed pinion I" and 2 respectively and all these pinions which are identical with one another engage in a toothed crown 4, supported so as to be capable of turning by the plate or arm 3. The plates l, I and 2, 2, of each pair are provided with crank pins la, la and 2b, 2b respectively, which are adjustable in position in a radial direction and to which are pivoted respectively the crossed rods 5 and 6.

The crank pins la, la are situated at the same distance from the axis of rotation l of the corresponding crank I. In a similar manner the crank pins 2b, 2b are situated at the same distance from the axis of rotation 2 of the corresponding crank 2.

Upon the crossed rods 5, 6, which must naturally be arranged in two distinct planes, so that one will not impede the movements of the other, is mounted at the point of intersection a member 1, adapted to slide on both rods 5 and 6 at the same time.

From the constructional point of view the cranks I, 2, have the form of forks as will be seen in Figure 4, which illustrates one of the cranks 2.

Between the two arms of the fork is arranged a screw 8, mounted so that it can turn by means of its end pivots 8', 8 in the end of the fork and in a cross member 9, which serves to close the end of the fork. The rod I0 of the crank pin 2b to which the rod 6 is pivoted engages with the screw 8, which can be rotated by means of the end knob 8a, so that this pin can thus move radially merit of translation in the direction of the axis y along the crank in order to place it at a predetermined distance from the axis of rotation of this same crank or if desired in order to make it coincide with this axis.

A scale I I is engraved upon one of the .arms of the crank, and a pointer l2 rigid with the pin enables the position of the crank pin with respect to the axis of the crank to be established accurately. l

The crank 2 bearing by its flange I3 upon-the supporting plate 3 is mounted so that it can turn with its pivot 2' in a suitable hole in the plate itself, while below the latter upon an extension of the pivot 2' is keyed the pinion '2" adapted to engage with the toothed crown 4.

The intersection member 1 slidably mounted upon the two rods 5, 6, is preferably formed by a sleeve having a closed end (see Figure 3) in the peripheral wall of which .areiormed at different heights two pairs of holes through which the said rods pass.

The method of use and of operation of the apparatus described above is as follows It is assumed that the crank pins la, la, of the cranks 'I have been moved to a distance a from the axis of rotation of these cranks and the pins 2b, 2b of the cranks 2 to a distance b from the axis of rotation? of the corresponding cranks.

When the four cranks turn while preserving their parallel relation the rods 5 and 6 which reproduce'straight lines A, A, and B, B, in Figure 1, move while always remaining parallel to their original direction'and each point on these rods describes a circle of radius a and b respectively. The point of intersection P of these rods conseduently'describes an ellipse e, having half axes a and b. Each point on the intersection member I which while moving along the rods 5 and B preserves an unvarying position with respect to the point P consequently describes the desired ellipse. Consequently if an arm provided with a tracing point is rigidly secured to the screw threaded'pivot 7 of this member "I, this point will trace the desired ellipse on the plane oi the draw: ing. If instead of a point the said arm is connected to a'working tool such as a milling cutter, this'tool canbe employed for reproducing the de-' sired ellipse on .a piece of work.

By changing the radii a, b of the cranks various ellipses'can be obtained. By making a=to b, the

' apparatus will trace a circle of radius r=a=bu If ais given any value and if b=0, that is to say if the pins 2b are made to coincide with the axis of rotation 2' of the cranks 2 (Figure 5) and further if the whole apparatus is given a moveirifsuch a manner that this .assembly travels over space's'propo'rtional to the angle of rotation of the cranks it is obvious that the tracing point secured to the intersection member 1 will trace a curve of equation x=a sin that is to say a sine rv In order to obtain such a movement of translation of the apparatus for example it may be guided By displacing the whole of the apparatus in the direction of the axis 1/ sine curves may be traced which are displaced relatively to each other by any quantities.

The translational movement of the whole of the apparatus instead of being obtained by means of a rack 14' and a pinion rigid with the pivot 2' may be obtained by means of a cable wound in one of the grooves of a cone of grooved pulleys keyed upon the pivot 2, the said cable being held in tension at its ends and arranged parallel to the axis 1/.

If in the apparatus mounted, as in Figure 5,

the pins 2b of the cranks 2 are moved to the same distance from the pivot 2 as the pins la are from 'I, that is to say if a is made equal to b, it is then possible to trace cycloids in which the radius of the rolling circles is r=a=b. I1 a=b r elongated cycloids are traced; if a;=b r shortened cycloids are traced.

Finally if a b '1' an infinite variety-of curves can be traced, the general equation 0f Whichreferred to -the axes is x=a-a cos-, y== rb sin g5. e

The apparatus can also serve fordescribing an Archimedean spiral, the equation of which is r=c where c is a constant.

. For this purpose, the. radius'ofall the cranks must change proportionally to the angleptrotation In order to satisfythis'co-ndition, the cranks may be given the modified shape shown in Figure 6, in'which a bevelled pinion 15 is keyed upon the screwB, and engages with another bevelled pinion I 6 which is fixed andcoaxia-lwith the axis of rotation of the crank.

During the rotation of the cranks, the corresponding pinion l5 by meshing with-the fixed pinion IE will turn and'rotate the screw 8, so that the corresponding crank pin will move proportionally to the angleofrotation of thecrariks.

The tracing point secured to the intersection member I will consequently trace an Archimedean spiral. During this operation the base plate 3 must be maintained in a fixed position as is obvious.

The apparatus may advantageously be provided with a dividing device as shown in Figure 7,

This dividing device comprises an extension 11, adapted to bear upon the plane of the drawing and to which the base plate '3 of the apparatus is removably'connected in any suitable manner. The pinion 2" of one of the cranks engages an equal pinion l8, keyed upon the verticalsha'it l9, carried by the extension I1, and provided with a bevelled pinion zfl engaging in beve led in n ke ed po he-shah o a dividing drum 22. v

T surfa e i the drum ruponta plurality .of generating lines, is provided with :a number of various graduations, 12' 12", etc., which sub-l ivide the esponding generating lines into.;.a certain number of equalxpar-ts.

Each of these graduationscan beiread' through a slot 23' opposite referencev pointer lfia" on a slide block 23 movable in an axial directionrand provided with another reference pointer: .23;"' adapted to be brought into register withpthe graduations of a fixed scale 24, with the object of indicating thenumber ofsub-divisions of the graduations actually visible through'the slot,23

When. trac n an e psethe an the su iy i s h o en raduat m s su c iy l qnn lie ermint rii" s that it is possible to mark on the curve being traced the corresponding sub-divisions.

It is obvious that from the constructional point of view the apparatus may undergo numerous modifications and that the invention is in no way limited to the diagrammatic forms above illustrated and described.

Having now described my invention, what I claim as new and desire to secure by Letters Patent is:

1. In an apparatus for describing and tracing sine curves, cycloids and other curves, the combination with an ellipsograph of the type comprising a supporting frame, two pairs of parallel cranks rotating on two pairs of pivots fixed to the supporting frame and arranged in two axial planes perpendicular with each other, each of the cranks including an adjustable crank pin, two crossed rods each pivoted to the adjustable crank pins of a pair of cranks, and a sliding member bearing the tracing tool mounted in the point of intersection of the said rods, of guiding means associated with the ellipsograph whereby the apparatus can be given a movement of translation r in the direction of one of its axes and whereby its movement of translation can be controlled proportionally to the rotation of the cranks in order to trace sine curves or cycloids.

2. An apparatus according to claim 1, characterized by the feature that the whole of the ellipsograph by means of a slide block rigid with its supporting frame is mounted capable of being displaced in the direction of one of its axes along a. fixed guide, while the translation is obtained by means of a pinion rigid with one of the cranks of the ellipsograph and in engagement with a rack rigid with the said fixed guide.

3. An apparatus according to claim 1, characterized by the feature that a pinion is keyed upon the axes of each crank of the ellipsograph, the said pinion engaging with a toothed crown rotatably supported by the supporting frame of the ellipsograph, whereby the parallel relation between the cranks is maintained during their retation.

4. An apparatus according to claim 1, characterized by the feature that the pin of each crank engages with a longitudinal screw arranged between the two arms of the fork shaped crank and adapted to be rotated so as to displace the said pin with respect to the axis of rotation of the crank.

5. An apparatus according to claim 1, characterized by the feature that the pin of each 'crank engages with a longitudinal screw arranged between the two arms of the fork shaped crank and adapted to be rotated so as to displace the said pin with respect to the axis of rotation of the crank, the said longitudinal screw of each crank being provided with means adapted to rotate the said screw during the rotation of the crank itself, whereby an automatic displacement of the crank pin can be obtained.

6. An apparatus according to claim 1, having a. sliding member bearing the tracing tool mounted in the point of intersection of the two crossed rods of the ellipsograph, characterized by the feature that the said sliding member is provided with a screw threaded pivot on which an arm bearing the tracing tool is secured following any desired direction.

7. An apparatus according to claim 1, further comprising a separated dividing drum for effecting a corresponding sub-division of the curve being traced, and a transmission device between said drum and one of the cranks of the ellipsograph to control the drum.

ELIA AFRICANO. 

